SOLUTION: Please help me answer this question:
Without using a calculator, find the value of
tan6° x tan12° x tan18° x ••• x tan84°
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-> SOLUTION: Please help me answer this question:
Without using a calculator, find the value of
tan6° x tan12° x tan18° x ••• x tan84°
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Question 1155360: Please help me answer this question:
Without using a calculator, find the value of
tan6° x tan12° x tan18° x ••• x tan84° Answer by ikleyn(52799) (Show Source):
The key to the solution is this identity tan(x) = .
It gives
tan(6°)*tan(84°) = 1
tan(12°)*tan(78°) = 1
tan(18)*tan(72°) = 1
. . . and so on . . .
tan(42°)*tan(48°) = 1.
By multiplying all these identities, you will get finally
tan(6°)*(tan(12°)*tan(18°)* . . . *tan(84°) = 1.
ANSWER. This product is equal to 1.
